A Dynamic Method for Generating Multi-Resolution TIN Models

It is essential to generate multi-resolution Triangulated Irregular Network (TIN) models dynamically and efficiently in three-dimensional (3D) visualization, virtual reality, and geographic information systems (GIS), because the data that needs to be processed is multiple in scale and large in volume. This paper proposes a new method, which extends the edge collapse and vertex split algorithms, to dynamically generate a multi-resolution TIN models. In contrast to previous approaches, a new method is proposed to encode and store vertex dependency relationships in the multi-resolution model. As a result, the validity of vertex splits and edge collapses is improved; the efficiency of storing data is also enhanced by the proposed method. To evaluate the performance of the proposed method, we further extend the assessment to (a) time cost; (b) the quality of the multi-resolution TIN model; and (c) the view-dependent multi-resolution model. The root mean square error (RMSE) of the elevation of the vertex and the quality of the shape of the triangle are adopted to evaluate the quality of a generated multiresolution TIN model. The results of the experiment demonstrate that the proposed method performs better than previous methods in terms of time cost, and can achieve multiresolution TIN models with a higher accuracy. Introduction A Triangulated Irregular Network (TIN) is a popular model for representing terrain surfaces. It is widely used in GIS, computer graphics, and virtual reality (VR). This is because it offers such advantages as a simple data structure to efficiently represent features of terrain and can be easily rendered using common graphics hardware. To represent the details of a terrain, a high-resolution TIN model (with dense triangles) should be used. However, this will lead to the need to process a large volume of data and cost a great deal in terms of computation time. On the other hand, although a lower-resolution TIN can reduce the volume of data, the details of a terrain surface will be lost. Therefore, a multiresolution TIN model that can represent the details of a terrain on different levels using variable resolution according to different requirements would be a solution to this A Dynamic Method for Generating Multi-Resolution TIN Models Bisheng Yang, Wenzhong Shi, and Qingquan Li problem. A multi-resolution TIN model can precisely describe various levels of surface morphologies using an integrated TIN model with different resolutions. The multi-resolution TIN model should also preserve feature points (e.g., saddle points) and feature lines (e.g., the boundary of a terrain feature) at different levels of detail. A single-resolution TIN model has to consider a trade-off between computation time (e.g., the time required to interpolate a higher-density TIN model based on a lower-resolution one) and volume of data in the storing of a TIN model. A higher-resolution TIN model requires a larger volume for storing data, while a lowerdensity TIN model takes much more time in interpolation and computation to generate a higher-density TIN model. It is a fundamental issue for 3D visualization and analysis in a GIS to simultaneously visualize terrain in detail in 3D and to process the data at a rapid speed. This target can be attained using a multi-resolution TIN model, an efficient technique for the rapid rendering and visualization of a digital terrain in different resolutions without losing too many details of the corresponding terrain surface in the real world. A Review of Related Studies The multi-resolution model has been a focus of research in many areas, such as 3D compression, the visualization of terrain, the simplification of models, multi-resolution analysis, and progressive transmission. Several methods and algorithms have been developed for constructing multiresolution models (De Floriani, 1989; De Floriani et al., 2000; Eck et al., 1995; Lindstrom et al., 1996; Hoppe, 1996, 1998; Garland, 1999; Shi et al., 2002, 2003). A review and analysis of the existing solutions was given by Heckbert and Garland (1997). At present, there are three categories of algorithms that pertain to the multi-resolution model and that deal directly with triangle meshes. These are the algorithms that (a) simplify a mesh by removing the vertex; (b) simplify a mesh by removing the edge; and (c) simplify a mesh by removing triangulation (Ribelles et al., 2002). Other related studies include a multi-scale spatial database (Jones et al., 1992) and adaptive refining strategies (Zorin, 1997) based on a loop scheme. De Floriani et al. (2000) developed a system based on the hierarchical triangle model, which was proposed by De Floriani (1989) to construct multi-resolution TINs. Algorithms on hierarchy triangle models were addressed by Heller (1990), Soucy and Laurendeau (1992, 1996), De Floriani et al. (1996), Voigtmann et al. (1997) and Pedrini (2000). The principle of this category of algorithm is to iteratively insert a vertex into the regions of a TIN model PHOTOGRAMMETRIC ENGINEER ING & REMOTE SENS ING Augu s t 2005 917 B. Yang is with the GIS Division, Department of Geography, University of Zurich-Irchel, Winterthurerstr. 190, CH-8057 Zurich, Switzerland ([email protected]). B. Yang and W. Shi are with the Advanced Research Center for Spatial Information Technology, Department of Land Surveying and Geo-Informatics, The Hong Kong Polytechnic University, Hong Kong. Q. Li is with the National Key Lab for Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, Wuhan, China. Photogrammetric Engineering & Remote Sensing Vol. 71, No. 8, August 2005, pp. 917–926. 0099-1112/05/7108–0917/$3.00/0 © 2005 American Society for Photogrammetry and Remote Sensing 03-052.qxd 1/13/04 10:54 AM Page 917